{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hierarchical clustering avoids the need to specify a target number of clusters because it assumes that data can successively be merged into increasingly dissimilar clusters. It does not pursue a global objective but decides incrementally how to produce a sequence of nested clusters that range from a single cluster to clusters consisting of the individual data points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While hierarchical clustering does not have hyperparameters like k-Means, the measure of dissimilarity between clusters (as opposed to individual data points) has an important impact on the clustering result. The options differ as follows:\n",
    "\n",
    "- Single-link: distance between nearest neighbors of two clusters\n",
    "- Complete link: maximum distance between respective cluster members\n",
    "- Group average\n",
    "- Ward’s method: minimize within-cluster variance\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.891359Z",
     "start_time": "2020-06-18T22:12:15.391052Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage, cophenet\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "from sklearn.metrics import adjusted_mutual_info_score\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.datasets import load_iris\n",
    "from scipy.spatial.distance import pdist\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.894468Z",
     "start_time": "2020-06-18T22:12:15.892441Z"
    }
   },
   "outputs": [],
   "source": [
    "cmap = ListedColormap(sns.xkcd_palette(['denim blue', \n",
    "                                        'medium green', \n",
    "                                        'pale red']))\n",
    "sns.set_style('white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.905839Z",
     "start_time": "2020-06-18T22:12:15.895434Z"
    }
   },
   "outputs": [],
   "source": [
    "# if you have difficulties with ffmpeg to run the simulation, see https://stackoverflow.com/questions/13316397/matplotlib-animation-no-moviewriters-available\n",
    "# plt.rcParams['animation.ffmpeg_path'] = your_windows_path\n",
    "plt.rcParams['animation.ffmpeg_args'] = '-report'\n",
    "plt.rcParams['animation.bitrate'] = 2000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Load Iris Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.916033Z",
     "start_time": "2020-06-18T22:12:15.906735Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename'])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = load_iris()\n",
    "iris.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.922928Z",
     "start_time": "2020-06-18T22:12:15.916989Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Create DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.935751Z",
     "start_time": "2020-06-18T22:12:15.923993Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 150 entries, 0 to 149\n",
      "Data columns (total 5 columns):\n",
      " #   Column             Non-Null Count  Dtype  \n",
      "---  ------             --------------  -----  \n",
      " 0   sepal length (cm)  150 non-null    float64\n",
      " 1   sepal width (cm)   150 non-null    float64\n",
      " 2   petal length (cm)  150 non-null    float64\n",
      " 3   petal width (cm)   150 non-null    float64\n",
      " 4   label              150 non-null    int64  \n",
      "dtypes: float64(4), int64(1)\n",
      "memory usage: 6.0 KB\n"
     ]
    }
   ],
   "source": [
    "features = iris.feature_names\n",
    "data = pd.DataFrame(data=np.column_stack([iris.data, iris.target]), \n",
    "                    columns=features + ['label'])\n",
    "data.label = data.label.astype(int)\n",
    "data.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Standardize Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The use of a distance metric makes hierarchical clustering sensitive to scale:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.946377Z",
     "start_time": "2020-06-18T22:12:15.937128Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "features_standardized = scaler.fit_transform(data[features])\n",
    "n = len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Reduce Dimensionality to visualize clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:15.978663Z",
     "start_time": "2020-06-18T22:12:15.947415Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "features_2D = pca.fit_transform(features_standardized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:16.187490Z",
     "start_time": "2020-06-18T22:12:15.979594Z"
    },
    "hide_input": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ev1, ev2 = pca.explained_variance_ratio_\n",
    "ax = plt.figure(figsize=(14, 6)).gca(title='2D Projection',\n",
    "                                     xlabel=f'Explained Variance: {ev1:.2%}',\n",
    "                                     ylabel=f'Explained Variance: {ev2:.2%}')\n",
    "ax.scatter(*features_2D.T, c=data.label, s=25, cmap=cmap)\n",
    "sns.despine()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Perform agglomerative clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:16.191618Z",
     "start_time": "2020-06-18T22:12:16.188347Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.01000000e+02, 1.42000000e+02, 0.00000000e+00, 2.00000000e+00],\n",
       "       [7.00000000e+00, 3.90000000e+01, 1.21167870e-01, 2.00000000e+00],\n",
       "       [1.00000000e+01, 4.80000000e+01, 1.21167870e-01, 2.00000000e+00],\n",
       "       [9.00000000e+00, 3.40000000e+01, 1.31632184e-01, 2.00000000e+00],\n",
       "       [0.00000000e+00, 1.70000000e+01, 1.31632184e-01, 2.00000000e+00]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = linkage(features_standardized, 'ward')\n",
    "Z[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:16.204537Z",
     "start_time": "2020-06-18T22:12:16.192509Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 149 entries, 1 to 149\n",
      "Data columns (total 4 columns):\n",
      " #   Column     Non-Null Count  Dtype  \n",
      "---  ------     --------------  -----  \n",
      " 0   cluster_1  149 non-null    int64  \n",
      " 1   cluster_2  149 non-null    int64  \n",
      " 2   distance   149 non-null    float64\n",
      " 3   n_objects  149 non-null    int64  \n",
      "dtypes: float64(1), int64(3)\n",
      "memory usage: 4.8 KB\n"
     ]
    }
   ],
   "source": [
    "linkage_matrix = pd.DataFrame(data=Z, \n",
    "                              columns=['cluster_1', 'cluster_2', \n",
    "                                       'distance', 'n_objects'],\n",
    "                              index=range(1, n))\n",
    "for col in ['cluster_1', 'cluster_2', 'n_objects']:\n",
    "    linkage_matrix[col] = linkage_matrix[col].astype(int)\n",
    "linkage_matrix.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:16.250724Z",
     "start_time": "2020-06-18T22:12:16.205709Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cluster_1</th>\n",
       "      <th>cluster_2</th>\n",
       "      <th>distance</th>\n",
       "      <th>n_objects</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>101</td>\n",
       "      <td>142</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>39</td>\n",
       "      <td>0.121168</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10</td>\n",
       "      <td>48</td>\n",
       "      <td>0.121168</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9</td>\n",
       "      <td>34</td>\n",
       "      <td>0.131632</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0.131632</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cluster_1  cluster_2  distance  n_objects\n",
       "1        101        142  0.000000          2\n",
       "2          7         39  0.121168          2\n",
       "3         10         48  0.121168          2\n",
       "4          9         34  0.131632          2\n",
       "5          0         17  0.131632          2"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linkage_matrix.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:16.596455Z",
     "start_time": "2020-06-18T22:12:16.251604Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linkage_matrix[['distance', 'n_objects']].plot(secondary_y=['distance'],\n",
    "                                               title='Agglomerative Clustering Progression',\n",
    "                                               figsize=(14, 4))\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compare linkage types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hierarchical clustering provides insight into degrees of similarity among observations as it continues to merge data. A significant change in the similarity metric from one merge to the next suggests a natural clustering existed prior to this point. \n",
    "The dendrogram visualizes the successive merges as a binary tree, displaying the individual data points as leaves and the final merge as the root of the tree. It also shows how the similarity monotonically decreases from bottom to top. Hence, it is natural to select a clustering by cutting the dendrogram. \n",
    "\n",
    "The following figure illustrates the dendrogram for the classic Iris dataset with four classes and three features using the four different distance metrics introduced above. It evaluates the fit of the hierarchical clustering using the cophenetic correlation coefficient that compares the pairwise distances among points and the cluster similarity metric at which a pairwise merge occurred. A coefficient of 1 implies that closer points always merge earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:16.599895Z",
     "start_time": "2020-06-18T22:12:16.597578Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "methods = ['single', 'complete', 'average', 'ward']\n",
    "pairwise_distance = pdist(features_standardized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:24.543505Z",
     "start_time": "2020-06-18T22:12:16.601016Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qq8uoATEbLgMY27ZtU7t27SRJcXFx+u6776yW7969WxkZGcrNzVVCQoIef/zxwLS0lLmbReBOR5sOs2cC/VQoEE9uSrNKvy+MmNIeiozyhN+fvB2yIpXePntSTNLXoUtl8RwDALxgtCFARhcinWCELpcBjLy8PEVbPMGKiIjQhQsXzPOyd+/eXSkpKYqOjtaQIUO0du1atW/fPnAtLkX+6kgbJdXRlFViW2si3LJDAiHQVfr91ZkyYkq7K/Zm7gh2B9JIT/j9xZshK1Jgh3zYO8+lVUyyLJ5jAACAUOcygBEdHa38/Hzz95cuXTIHL4qKivTwww+rSpUqkqT4+Hjt2bPHbwEM2w53xrYMOto+sJdVQnaI/3jasfKk0+bPzpQRU9qdse1YG6UDaYTipP7m6ZAVyT/7bNRpOsviOQZQBvhal8Ef9ROocQAgSFwGMJo3b661a9eqW7duysrK0m233WZelpeXpx49eujzzz9XpUqVtGXLFiUlJfmtcZYdblORRjravrHNKjFKdkg48rTTFs6dKct9D5d9DjdM0wkAbvK1LoOv9ROocQAgiFwGMDp37qxNmzbpwQcfVFFRkSZOnKgVK1bo3LlzSk5O1jPPPKP+/fsrKipKd9xxh+Lj4/3aQFOHO1w72rbFRO1NNRqKQ0AcFUl1NZWqL/tqxCE0Rui0MdY/NNmrWeGoVoW/z2MoXTP+aGuw9teTLC2mRwXCTDDrMlDjAEAQuQxglC9fXhMmTLB6rW7duub/JyYmKjEx0f8tg6SSwz5si4aG6hAQR0VSnRVF9XVfGUJjH2P9Q5O9mhWm/x8vKFBOQYEk6czFi+apY/3VqQ2la8YfbQ3W/nqSpeXr9KhGrDUDAABgy2UAA8HnrJhoKGemeFok1R/76vEQGtM4U1O6ZEZGmUyZDOfhKZLr2VmM2pFzVLMiYft25RQUBLSzbdq2vWNntM6vP67vYP2OeJKl5cv0qEatNQMAAGCJAAbgjOU406ys4u9dBDAC/SQzlNL3bdk7NpL37fbX+pzNzhKqHTl3Or7+uJbczRLgCX8xI//+UmsGAMoIXwu9+sIfRWJ9QYHZMo8ABpyyrFVhWTsiFOtueM00ztTNP8SBfpIZSun7tuwNe/Cl3f5cn7NshrLKX9eSO8ESozzh93cQzVOh/PsLoIxzt9PrSQeVzmRw+Fro1RfB2KYJBWbDAgGMAHHU8ZdCq+imZd0IU+0Ie3UjCHRYC/STzFAe8uHvwqVGKIQaykrzWjLCE35/BL18DYLYHnNTAU4jDr8BEEbc7fS620GlMxlcwSz0GiwUmA0LBDACxF7HXwrNopHu1I1wN9ABAMHma9ArEJlEpnaRiQEgqPzZ6aUzCSAACGAEkL0ilf4oRGnU7A6PC2Si1Lhbf8CTaRvLutKqZWJaf8axY2F3jENZoDKJjJ5BRC0TAEDAeVvDw9v6Gwx1CikEMGQdEDCxDQyYGGFIRFnK7ggW0zk3HbOMbRll+ri5W3/Ak2kby7rSrGVimuY03I4xQo9RapkAAMowb2t4eFN/g6FOISdkAxi2HVBfMhAsAwImlv83MVKAwDLbwTYjI5DZGBnbMkqlxkWgg0qW5zzrRJYyd2Ua4rx6ypOMCXfrD1BT4rLSqmUSzsfYFk/4jc8ItUwAIKx4mpFQFjIRSquGB0OdQk7IBjDsBR18CTDYG+5hy9shEYEe8uHvY+FqW5LMHf9AbMO0nUAHlUzn3ChDXUyF/CT3O21kTFwWDh3fQA/xCfYMHVLpPuEvzWuGIUMIZ/YeSvjC0QMNb/n1YYxtR9O2I2mkDmI4Ko1AQCDOsacZCWQioAwL2QCG5F7NBV8zBvwRfCiNIR+lWX+itDr+gQwqGZG3hfzImCgWDqntgQ5Y+bs4pbdK6wl/aV4zDBlCOLP3UMIX/lqPFIAHPrYdTcuOJB3E4At0ICCQ5zjQGQlkIiBEhHQAwx2+ZgzYBh+Onz2urBNZOvPHGfPQA8l1MCNQBT29ZW8IjhHqe4Q7ow0p8CYrJJiCldru78wFZ8fdch8DMf2mrwExrhnX2zLK73c48zUjwNcMgHD8vHXnoUQwBORezFFHkw6iMQQyEMA5hlF4UwjVKBlHLpSJAIargoy+ZgxYfugmzElQTn6O4mvFm5cbqTaGu2yfhoTiPiDwwmF6R390uIM1rWYgz4+3wyvC4ZoJllALDhmZrxkBvmQA8HkLAGWYs8CBqwCBP4MB3hRCNVLGkRNlIoBR2gUZy8p0obaBmVBh1Glky6qy/tTYXx3uYE2rGajz48vwirJ+zQQLwSH/ClZGQGl93jrLMnGWQcLnKNziztNdd5/mUhcEZYmzwIGzAEEgggFldNhRmQhgSMYryAjPOQpM2N5MMY0s/K2sd7i9fXLPbBPGU9avVfiPsywTRxkkfI7Cbc46acePS/8LuEq63DGz58yZ4uXuproT7PCMJ8MIPB0+wLlwzJvAAcOP3FZmAhjB4G0dCX9OAWtUjoqnOjtm9gITjm6mjFZTBDAyntwHDrOLwJar+hru1s/wxz2Bp1kmfI7CI85qfeTkeDcThjMUQfWcJ8MIPDlfoXguHAVzSnNYB/wibAMY7j7td8bbOhKlOe1psDgqnurqmHk6PIfhJIB7eHIfGMwuAluu6mu4Uz+jrN0TBJu3w2kkP9xLWHaawmlK1UCkrvOE2jtGPheeBhV8+Z1xFMwp7WEd3jIdq9L6O2LgYWJhG8Dw5Gm/M97WkTD9nG0H3LYAqadcFTQtTY6G9fiz9gbDSaxR5C/4eCIffggOGYe7s4sEOgvC1/oaZEL4lzfDaSQ/3UtYdpqYUjX0uerU8TTfM54EFfzxO+NpMCeQQTPba8lVYMLesQrk3xF3snfcydoJQBvDNoAhWd9gmIY8ZJ3IKtUpRZ0VIHU0DMPb9YUST4bn2J5HfwaEQg1DBYKPJ/Klw9tZUlC2uTu7CFkQ1jwd2urpNLTeTjvrz3sxb4JKfgsk2es0GSWbwIgZIkZO9XfVqTO9blsHRHJc7yPcgxruBhWM8jtjjze/R7bXkjuBCdtjFehj4k32jr3f36ws67b6eM2HdQDDkqMhD6XBUaaCt20qCwVN/TE8J5QDOL7gaXDwcQ4Cz5dZUlC2+ZL9YNsxNz3UMCmrQxM9Hdrq6TS0lu87fva4cvJznLy72Jk/zpg/x50pq+dEUul05I2YIeLvVH9/BGls0/dNHP28u3VAjJqJE66ZJp5mRZh4+3vkrI5MqHIWmJH8cs0TwLBgxI6/EdtUWnwdnhOOxwwIJ8ySAn9zNCxRCo2MDF/qQnlag8rbQFHCnATl5Oe4Hfxwxp/nxF5WiaPMkVILmjjryB8/bn92D2+e8hsxQ8Sfqf6Wx7FGjeLAQlZWyWPl7Bh5k77vzj74+zh72wG35W6miT1GDcq4w5usCBMj/h65y1HWhORdHRJn174fjgkBDAAAgP9x1DEPhaC4bQDm+NnjyjqRVSKbIdhZC77WCDFxdk48LdZuL6vEXpDFp6CJo0wAT4MLpp9zd6YPdzuU3rTP9udsf9YkEE/kPWmv6Tg6Om7uHCPTOmy3684xKi32OuCmYJcnARvTz3o6fEByr4PqbkHKYAxxst1vb893RoZnv0eW2/L053xlL2AVqDokfkAAAwAAhKxAz0YVqKnPvZ0Zw5NMClO2Q3yt+BLrdrQOfxYD9ySrQXLvmLobmPCmWLs7gRWfAln20sx96RA462DaCyq46gx52z5nnWbJflaIPzqq3rbX8rjZ65w626a9/bXcpqcdc9P7MjIcHw/LbbjTPnt1EnJypPjLfwfsHidfggX2frZevct1QOLirNfhbkaLs+yZb76RXnjh8vpN/N3hd3a+Xf2cqW2urhFTm93dlrN1eDtbiaO/J+7+LXGnTVLxeSsokGJiLm/XnfZZIIABAABClmVHtUblGsrJz/Fr1oG79SE8DXR4MzOGr7OlWbbLEVfFxU3LCy4WKGZyjHkb9vbT3awGT/bNXpbJ+sPrzW21bIen++6IvaBJvfR6VkNh3L6+fC3C527nxF+d+6ws94IfjjrNlh1LU2FLU0DDsi3uDPNwllnh7VNyb2d2sNxfy3PoTcfctH/OZpxwlEnhrNNquf/uHCdvz4Ftey2vt7w8KTra/jFw93fBUfaM5fqdHWt3OcuYcHS+XQWiLNtu4ipI4Whblpytw91r0FFQwTag4O7fEnfbFBVVvC1LHp638q7ecOnSJY0bN07JyclKTU3V4cOHrZavWbNGSUlJSk5O1oIFC9zaKAAAgC1X9xyOmDqq11e53vx9fK141ahcQ1knsrT+8Hq9sOoFJcxJUMKcBGVsy7D6+YxtGUqYk2Cejcx2uWn9KY1TzK/Zvs82kGK5Xcv3WW7LUkrjFK0bsM78ZdqWqU3Hzx6XJH1z9BvFTI5RzOQYh/tjj6t9tLe/tsEGy32MiohSXkGeuY2WmRae7qMkFVws0MafNrq1b6b2mc551SuqWgVcHO2/5Wxz7hwz2/02bTvuujjl5Oc43H+32QYIMjIuv56QYH+ZbSczK0tav774SbTl+6TLHaGUy8e5xPqc7rjNE2RnRR3tMW3f9HV98e+nORPAdn2m95veFxcn3XZb8f8d7aNlWy07WZ6017ad7gzLcWd9ro676X2227PsSEvF67E9frb76O7+u3qfvXMQH198rdk7B5bXqm174+Kktm2l06d9P6a27bNdv+2xtjzO9n6f7F1H3lzvtp12b645b4+Ns3W4cw1aBl6ioqx/3tF14e417axNlufN8tx58LfJZQDjq6++UkFBgebPn6/nnntOkydPNi8rLCzUpEmTNGvWLM2dO1fz589Xbm6uy40CAADYcnbP4S7bzq0kh8EMUyfWNlPAUWfU1ftsAymmoRuW73M30GHZac4ryDM/7bcMHEjud57d3UdXLIMbbWPb6vSI004DHe7uY1SE9Q20KbPC9ly5apMjtjO7mb63DexYbss2EGMZgDHtv6vtOuWow+RpJ9Neh9Z2O7527t3tZDkLvniyPk/30fJn/BGE8Advj7uzjrQ7HURX++/N+66/Xqpa1fvAiTO214w7wTVbzgIJzoJ+ttvy9Hr39mdKi7t/SyyDCs72xR/n2946TW1xc30uAxjbtm1Tu3bt/rfeOH333XfmZdnZ2YqNjVXVqlUVFRWlFi1aaOvWrV62HkC4Sdi+XVl5ecrKy2MWCQBO7zm8ZRlUOPPHGcXXilfcdXFaf3i9VSfenU6wv95nr01n/jhjNyByesRptY1tazdw4Gnn2d22+4Mn+2i7X6dHnLbKprE9V762yXL/M3dlav3h9ebMCsttWS6z13a/cNT5CWRnNJAdrczM4s6hqYOzfr3vHZzSDEzYBl985W3bjdgp9vVadcTymjlzxvvrxdkxswyInTlTHBDzZVuhxN+/P4H4ffTwei9XVFRU5OwNo0eP1j333KP4/6V7JSQk6KuvvlJkZKS2bt2qjz/+WG+++aYk6a233lLNmjXVt29fh+tr06aNbrjhBjf3BgAAGN3VV1+tDz74wOf1OLvnsId7CgAAyh5n9xUui3hGR0crPz/f/P2lS5fMNxK2y/Lz81WlShWn69uyZYtbjQYAAOHF2T2HPdxTAAAQXlwOIWnevLk2bNggScrKytJtpmI6kurWravDhw/r9OnTKigo0NatW9WsWbPAtRYAAJRZzu45AAAAXA4huXTpkl566SX98MMPKioq0sSJE7Vnzx6dO3dOycnJWrNmjd555x0VFRUpKSlJDz300P9v7+5ZWgmiAAwftRASTBqjJKAWkkYsrEVBIRYWQWxEEJRg7AQbO8E6QRA7Kxt/gf/A2sLCxsIujd+NqJ0wtzLsDbubzc7s7qx5n2rDHGfOfJA5LIpx5Q4AAP4Qt5pjeno66bQAAIAlur7AAAAAAAAASFrXPyEBAAAAAABIGi8wAAAAAACA9XiBAQAAAAAArNf136ia9vLyIo1GQ/L5vIyPj8vDw4Pk83kpl8tSqVRc20zHxTkWuadrjltbW9JqteTg4ECurq5ERP777PVsW9zx8bFcXl5KJpORgYEB+f7+lkwmI6VSSfb391Ob+/z8vGubX5xzznt7ezIzM9Nzf841c+bntp5B1+K3rTMn2/Yn6Jr5rZOJfex2jnXOVi/j6uaeVFzUY/3uSdycNYWN91ka7r1+zj3qOZbLZVlYWDD6PW2ij17jTNUUtuWuW1OEvVf86hLdGkCnv7j2J+ia6dYUYeu8pM6WjXd7Url3rSlUzM7OztTt7a1SSqlKpaJubm6UUkrV63V1enrq2mY6Ls6xyD1dc3x8fFQnJydqc3NTKaXU6+tr+7PXs41x19fX6vPzUyml1NraWvu5VqulOnevNr8455xXV1dD9eeVX2db0Dk62zpzsm1/gq6Z3zqZ2Ee/sXTPVi/j6vaRVFzUY9VqNZUEZ01h432Whnuvn3OPeo7b29uq2Wwa+5420UeYOBM1hY2569YUYe8Vv7rE9J1t4/7o1l5R3Hs2nC0b7/akcu9WU8T+JyTv7+9SLBbbn0dGRkREJJfLydPTk2ub6bg4xyL3dM1xeHhYDg8PJZPJiIhIoVBof/Z6tjFuaWlJstmsnJ+fy87OTvu5Wq2mOnevNr8455yLxWKo/rzy62wLOkdnW2dOtu1P0DXzWycT++g3lu7Z6mVc3T6Siot6rGq1Kklw1hQ23mdB42zMqR9yj3qOo6OjUq/XjX1Pm+gjTJyJmsLG3HVrirD3il9dYvrOtnF/dGuvKO49G86WjXd7Url3qylif4FRLBbl+flZRKT9qyIiIh8fHzI5OenaZjouzrHIPV1zzOVy8hd8fX3J0dGRzM3NycrKSvt5fX096dS68svdq80vzjnnn5+fUP155WdiPTtzsk3QNfNbJxP7aOIcmxhXt4+k4qIeK6mz66wpbLzP0nDv9XPuUc/xr9QV1BTe33Wm6xJdttcUIsHXLMjPmLr3TM7jL93tSeXebU8GlFIq1K6F9Pb2Jo1GQ7LZrExNTcn9/b1ks1mZnZ2V5eVl1zbTcXGORe7pmuPGxoaIiOzu7srFxUX73Do/ez3bFDc2NiatVktKpZLc3d1JoVCQUqkkQ0ND0mw2U5v74OCga5tfnHPOi4uLMjEx0XN/zjVz5ue1nkHXwi0n2/Yn6Jr5rZOJfQxyjsOerV7G1c09qbiox3LuSZycNYWN91ka7r1+zj3qOf7WFaa/p0300UucyZrCptx1v+vC3it+dYluDaDbXxz7E3TNdGuKsHVeUmfLxrs9qdy71RSxv8AAAAAAAADoFf9GFQAAAAAAWI8XGAAAAAAAwHq8wAAAAAAAANbjBQYAAAAAALAeLzAAAAAAAID1eIEBAAAAAACs9w/nOtPZbyEi5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x576 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(figsize=(15, 8), nrows=2, ncols=2, sharex=True)\n",
    "axes = axes.flatten()\n",
    "for i, method in enumerate(methods):\n",
    "    Z = linkage(features_standardized, method)\n",
    "    c, coph_dists = cophenet(Z, pairwise_distance)\n",
    "    dendrogram(Z,\n",
    "               labels=data.label.values,\n",
    "               orientation='top',\n",
    "               leaf_rotation=0.,\n",
    "               leaf_font_size=8.,\n",
    "               ax=axes[i])\n",
    "    axes[i].set_title(f'Method: {method.capitalize()} | Correlation: {c:.2f}',\n",
    "                      fontsize=14)\n",
    "\n",
    "\n",
    "sns.despine()\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different linkage methods produce different dendrogram ‘looks’ so that we can not use this visualization to compare results across methods. In addition, the Ward method that minimizes the within-cluster variance may not properly reflect the change in variance but the total variance that may be misleading. Instead, other quality metrics like the cophenetic correlation or measures like inertia if aligned with the overall goal are more appropriate. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Get Cluster Members"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:24.547594Z",
     "start_time": "2020-06-18T22:12:24.544439Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n = len(Z)\n",
    "from collections import OrderedDict\n",
    "clusters = OrderedDict()\n",
    "\n",
    "for i, row in enumerate(Z, 1):\n",
    "    cluster = []\n",
    "    for c in row[:2]:\n",
    "        if c <= n:\n",
    "            cluster.append(int(c))\n",
    "        else:\n",
    "            cluster += clusters[int(c)]\n",
    "    clusters[n+i] = cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:24.559806Z",
     "start_time": "2020-06-18T22:12:24.548482Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[144, 124, 120, 143]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clusters[230]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Animate Agglomerative Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:24.566536Z",
     "start_time": "2020-06-18T22:12:24.560894Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def get_2D_coordinates():\n",
    "    points = pd.DataFrame(features_2D).assign(n=1)\n",
    "    return dict(enumerate(points.values.tolist()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:24.623842Z",
     "start_time": "2020-06-18T22:12:24.567749Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n_clusters = Z.shape[0]\n",
    "points = get_2D_coordinates()\n",
    "cluster_states = {0: get_2D_coordinates()}\n",
    "\n",
    "for i, cluster in enumerate(Z[:, :2], 1):\n",
    "    cluster_state = dict(cluster_states[i-1])\n",
    "    merged_points = np.array([cluster_state.pop(c) for c in cluster])\n",
    "    cluster_size = merged_points[:, 2]\n",
    "    new_point = np.average(merged_points[:, :2],\n",
    "                           axis=0,\n",
    "                           weights=cluster_size).tolist()\n",
    "    new_point.append(cluster_size.sum())\n",
    "    cluster_state[n_clusters+i] = new_point\n",
    "    cluster_states[i] = cluster_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:24.638373Z",
     "start_time": "2020-06-18T22:12:24.624721Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{15: [-2.2622145316010216, 2.686284485110592, 1.0],\n",
       " 41: [-1.8581224563735717, -2.337415157553348, 1.0],\n",
       " 60: [-0.11019628000062932, -2.6540728185365645, 1.0],\n",
       " 62: [0.5621083064431792, -1.7647243806169446, 1.0],\n",
       " 106: [0.36701768786072436, -1.5615028914765063, 1.0],\n",
       " 108: [2.006686467676607, -0.7114386535471587, 1.0],\n",
       " 109: [2.2597773490125017, 1.9210103764598867, 1.0],\n",
       " 114: [1.4676452010173247, -0.44227158737708266, 1.0],\n",
       " 176: [0.28711522075373114, -0.24204262329732348, 2.0],\n",
       " 179: [-2.2058211672986987, -0.09844552008358048, 2.0],\n",
       " 185: [0.9688104990917799, 0.01907915384081543, 3.0],\n",
       " 194: [0.7389335833626245, 0.6838170188840107, 2.0],\n",
       " 197: [2.3691965862739517, 0.33967500639352843, 2.0],\n",
       " 198: [-2.4657912495858, -0.9936714816693262, 3.0],\n",
       " 205: [1.9290326043911596, 0.5634757376107679, 3.0],\n",
       " 206: [-1.9303546578375999, 0.4980362956076001, 3.0],\n",
       " 208: [-2.3324410024278306, 0.10599232941089061, 3.0],\n",
       " 209: [2.365628354573734, 2.5914923595139356, 2.0],\n",
       " 210: [-2.3753778947842483, -0.428476399606261, 5.0],\n",
       " 211: [2.775321891622194, 0.8286062652623241, 2.0],\n",
       " 212: [1.3703381593353579, -0.4066353802439459, 3.0],\n",
       " 214: [1.4771264049002877, 0.6845006301068535, 2.0],\n",
       " 215: [0.6124063740956357, -0.11263115492758463, 4.0],\n",
       " 217: [-2.107918266740138, -0.5961767325807753, 7.0],\n",
       " 218: [-2.2074608511148277, 0.39185352432566406, 7.0],\n",
       " 219: [-2.530562663777726, 1.9721518667486764, 2.0],\n",
       " 222: [-1.9447561950630023, 0.26668291555609785, 3.0],\n",
       " 224: [1.1317839552605031, -0.7225792577873079, 2.0],\n",
       " 225: [0.17415501993333077, -0.9041186723104582, 4.0],\n",
       " 226: [1.9804041815154314, 0.5524627673500003, 3.0],\n",
       " 228: [0.5970487156101139, -0.2629983547610023, 4.0],\n",
       " 229: [1.5978708558106194, 0.9834189460574745, 3.0],\n",
       " 230: [1.944288880741274, 0.9602696562701191, 4.0],\n",
       " 231: [1.066723936158902, 0.6275964565840024, 4.0],\n",
       " 232: [-0.43239104859121186, -1.8051529981646477, 3.0],\n",
       " 233: [1.3993792903437394, -0.9150062688479023, 2.0],\n",
       " 236: [0.20202521219193983, -1.5042170574230862, 5.0],\n",
       " 237: [1.1777972305328468, -1.5706593008861836, 3.0],\n",
       " 238: [1.9089871295906673, 0.7850341610197987, 2.0],\n",
       " 239: [-2.5638395941372223, 0.5658239416152503, 3.0],\n",
       " 240: [0.5834108821437097, 0.6210769014326585, 2.0],\n",
       " 241: [1.8396217867683873, -0.02362196158643326, 3.0],\n",
       " 242: [1.4274899699312786, 0.24628913465740437, 5.0],\n",
       " 243: [0.19303006787186602, -1.003259039619637, 3.0],\n",
       " 244: [3.1041735373340296, 0.2157110044581378, 2.0],\n",
       " 245: [0.16678817742501761, -0.402792363931369, 6.0],\n",
       " 246: [-2.2446551194172795, 1.0593800316735267, 6.0],\n",
       " 247: [1.1384647649646227, -0.7829411177202094, 4.0],\n",
       " 248: [-2.0951328107676597, 1.5594656985593047, 4.0],\n",
       " 249: [1.049661370014735, -0.05911604365815985, 5.0]}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster_states[100]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Set up Animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:24.674077Z",
     "start_time": "2020-06-18T22:12:24.639225Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "fig, ax = plt.subplots(figsize=(14, 6))\n",
    "ax.axes.get_xaxis().set_visible(False)\n",
    "ax.axes.get_yaxis().set_visible(False)\n",
    "\n",
    "sns.despine()\n",
    "xmin, ymin = np.min(features_2D, axis=0) * 1.1\n",
    "xmax, ymax = np.max(features_2D, axis=0) * 1.1\n",
    "ax.set(xlim=(xmin, xmax), ylim=(ymin, ymax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:26.044381Z",
     "start_time": "2020-06-18T22:12:24.675604Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scat = ax.scatter([], [])\n",
    "\n",
    "\n",
    "def animate(i):\n",
    "    df = pd.DataFrame(cluster_states[i]).values.T\n",
    "    scat.set_offsets(df[:, :2])\n",
    "    scat.set_sizes((df[:, 2] * 2) ** 2)\n",
    "    return scat,\n",
    "\n",
    "\n",
    "anim = FuncAnimation(fig,\n",
    "                     animate,\n",
    "                     frames=cluster_states.keys(),\n",
    "                     interval=250,\n",
    "                     blit=False)\n",
    "\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Scikit-Learn implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:26.048850Z",
     "start_time": "2020-06-18T22:12:26.045359Z"
    }
   },
   "outputs": [],
   "source": [
    "clusterer = AgglomerativeClustering(n_clusters=3)\n",
    "data['clusters'] = clusterer.fit_predict(features_standardized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:26.130480Z",
     "start_time": "2020-06-18T22:12:26.049720Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=2, figsize=(14, 6))\n",
    "\n",
    "labels, clusters = data.label, data.clusters\n",
    "mi = adjusted_mutual_info_score(labels, clusters)\n",
    "\n",
    "axes[0].scatter(*features_2D.T, \n",
    "                c=data.label, \n",
    "                s=25, \n",
    "                cmap=cmap)\n",
    "axes[0].set_title('Original Data')\n",
    "axes[1].scatter(*features_2D.T, \n",
    "                c=data.clusters, \n",
    "                s=25, \n",
    "                cmap=cmap)\n",
    "axes[1].set_title('Clusters | MI={:.2f}'.format(mi))\n",
    "for i in [0, 1]:\n",
    "    axes[i].axes.get_xaxis().set_visible(False)\n",
    "    axes[i].axes.get_yaxis().set_visible(False)\n",
    "\n",
    "sns.despine()\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Comparing Mutual Information for different Linkage Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:26.140527Z",
     "start_time": "2020-06-18T22:12:26.131344Z"
    }
   },
   "outputs": [],
   "source": [
    "mutual_info = {}\n",
    "for linkage_method in ['ward', 'complete', 'average']: \n",
    "    clusterer = AgglomerativeClustering(n_clusters=3, linkage=linkage_method)\n",
    "    clusters = clusterer.fit_predict(features_standardized)  \n",
    "    mutual_info[linkage_method] = adjusted_mutual_info_score(clusters, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T22:12:26.320598Z",
     "start_time": "2020-06-18T22:12:26.141434Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = (pd.Series(mutual_info)\n",
    "      .sort_values()\n",
    "      .plot.barh(figsize=(12, 4),\n",
    "                 title='Mutual Information'))\n",
    "sns.despine()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strengths and Weaknesses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The strengths of hierarchical clustering include that \n",
    "- you do not need to specify the number of clusters but instead offers insight about potential clustering by means of an intuitive visualization. \n",
    "- It produces a hierarchy of clusters that can serve as a taxonomy. \n",
    "- It can be combined with k-means to reduce the number of items at the start of the agglomerative process.\n",
    "\n",
    "The weaknesses include \n",
    "- the high cost in terms of computation and memory because of the numerous similarity matrix updates.\n",
    "- Another downside is that all merges are final so that it does not achieve the global optimum. - \n",
    "- Furthermore, the curse of dimensionality leads to difficulties with noisy, high-dimensional data."
   ]
  }
 ],
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